Chapter 9
Team Projects

T18. St. Petersburg paradox.
a. Suppose that you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads and nothing if it comes up tails. What is the mathematical expectation for this game?

b. Suppose that you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. Continue in this fashion for a total of 10 flips of the coin, after which you receive nothing if it comes up tails. What is the mathematical expectation for this game?

c. Suppose that you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. Continue in this fashion for a total of 1,000 flips of the coin after which you receive nothing if it comes up tails. What is the mathematical expectation for this game?

d. Suppose that you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. You continue in this fashion until you finally toss a head. Would you pay $100 for the privilege of playing this game? What is the mathematical expectation for this game?

REFERENCES:
See Martin Gardner's Mathematical Puzzles and Diversions (New York: Simon and Schuster, 1959, p. 145) for a discussion of the problem.


T19. We see examples of probability every day. Weather forecasts, stock market analyses, contests, children's games, television game shows, and gambling all involve ideas of probability. With your team members, search current newspapers and magazines to provide examples of probability. After looking for at least a week, collate your material to present a portfolio of the examples you have found.